Question

Which expression is equivalent to \frac{r^9}{r^3}

Answer 1

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`\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup`

r^6

`\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup`

To simplify this we need to use the division property of exponents:

`\large\boxed{\mathtt{(x^m)/(x^n) =x^(m-n)}}`. So if we divide two numbers with the same base, we subtract their exponents.

Let's apply this rule here.

`\twoheadrightarrow\sf r^9/ r^3`.

`\bullet` Since these two numbers have the same base, we subtract their exponents

`\twoheadrightarrow\sf r^6`

`\bullet` Great job! We found the answer

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Answer 2

Answer:
`(r^9)/(r^3) = r^(9-3) = r^6`

We subtract the exponents when dividing terms with the same base.

The general rule is
`(a^b)/(a^c) = a^(b-c)`